5 Tips to Avoid Careless Mistakes for Maths (Tip #1): Do NOT Skip Steps!
I believe many have heard maths teachers and tutors say over and over again: Do NOT skip steps! As a full time maths tutor myself, I say it too (guilty as charged), but only after convincing my students that it is absolutely critical that they do not skip steps in their working, especially if they are aiming for a distinction in both their E and A Maths papers, especially for A Maths.
There are in fact several reasons for not skipping steps, but pertaining to CSMs (Careless Stupid Mistakes) it is perhaps the best way to avoid arithmetic errors (i.e. operational errors when adding, subtracting, dividing, multiplying, etc.) and algebraic manipulation errors (i.e. expanding, simplifying and factorising) which are perhaps two of the most common types of CSMs out there. The probability of making a CSM goes up significantly when doing arithmetic operations or algebraic moves in your head, rather then penning down your steps. For those who don’t practice enough and lack mechanical fluency, the likelihood of making a CSM increases even more.
You may think you are saving time by omitting working steps, i.e. you equate fewer steps to less time, when in actual fact this is a huge misconception and worse still you do so at the expense of accuracy. Why? Well put it this way, writing down fewer steps does NOT equate to thinking in fewer steps.
This brings me to my main point: the reason why CSMs arise from skipping steps is simple – you’re trying to do too much mentally at one time. It actually takes a lot less effort and yes less time to just pen down each thought, i.e. one methodical step at a time. In other words, you can achieve both speed and accuracy by taking small quick steps, rather than taking large slow ones. The trick is to breakdown your mental thoughts into smaller, easier to manage pieces by penning them down fluently. Developing this one good habit alone can do wonders! 🙂